and the coincidence of two transmitted photonsfor different combinations of g is measured.

In our experiment, polarization-entangled photon pairs (uncorrected average visibility 97.99 T
0.03%) at 810 nm were created using a type II
nonlinear crystal in a Sagnac-type configuration
(26, 27). The SLM in the transfer setup is programmed such that the reflected photons acquire
l multiples of 2p azimuthal phase (l quanta of
OAM), which leads to complex patterns when
OAM is large (Fig. 1, B to D). Therefore, we
used a high-resolution SLM (1920 × 1080, full
HD; Holoeye Photonics AG, Berlin) with small
pixel size (8 mm). Nonetheless, for values of l ≥
300 we observed a clear reduction of mode transformation efficiency, which is the main limiting
factor (22). This is only a technical limitation that
can be overcome by higher-resolution SLMs or
novel techniques for creating photons with higher
l values (28). After the transfer setups, the modes
are enlarged to fit the masks (laser-cut black cardboard) and transmitted photons are focused to
bucket detectors.

As a demonstration of the flexibility of our
setup, we created two-dimensional spatial mode
entanglement with highly asymmetric OAM
states, in which one photon is transferred to l =
T10 and the second photon to l = T100 (Fig. 3A).
Because of its intrinsic conservation of angular
momentum, the SPDC process could not create
this asymmetric state directly. We then transferred
both photons to l = T100, showing the ability to
create OAM modes with very high difference
in quantum number (Fig. 3B). The highest value
of OAM per single photon where strong correlations were still measurable was l = T300 for
both photons (Fig. 3C). The decrease in mode
transformation efficiency of the SLM, however,
strongly affects the coincidence rate (about 1 coincidence count per minute in the maximum) and
therefore the statistical significance of our results.

To demonstrate successful transfer, we constructed an entanglement witness [similar to (29)],
which verifies entanglement if the sum of two
visibilities in two mutually unbiased bases is
above the classical bound of (21/2 + 1)/2 ≈ 1.21
(22, 29). The data for the visibilities were taken
in addition to the fringe measurements (apart from
l = T300) with longer integration. For the asymmetric OAM state l = T10/T100, we achieved a
witness value of 1.48 T 0.01. When both photons
were transferred to l = T100, the witness value
was 1.55 T 0.01. Both values were calculated
without any correction of the data and violate
the classical limit by ~30 standard deviations,
demonstrating the successful entanglement transfer. Because of the significantly smaller creation and detection efficiencies (hence a lower
pair detection rate) for l = T300, we corrected
for accidental coincidence counts (22), yielding
a value of 1.6 T 0.3 for our entanglement witness. With a statistical significance of more than
80%, we thus violate the bound for separable
states with photons that each carry l = T300
quanta of OAM.

Fig. 3. Measured coincidencecounts as a function of the angleof one mask and different anglesof the other mask. The measuredcoincidence counts (points) showa sinusoidal dependence (fittedlines) and depend only on the dif-ference between the angles ofthe masks, which is a clear signa-ture of nonclassical correlations.(A) The first photon is transferredto l = T10ℏ and the second tol = T100ℏ, showing the abilityto create asymmetric OAM entan-gled states. (B) Both photons aretransferred to l = T100ℏ. (C)Both photons carry l = T300ℏand nonclassical correlations canstill be measured. Here, the countrate decreased significantly (about1 coincidence count per minute)primarily because of limited con-version efficiency. The integrationtimes in (A), (B), and (C) were 2min, 9 min, and 64 min, respec-tively, for each data point. Errorbars in all plots (if large enoughto be seen) are estimated fromPoissonian count statistics.Fig. 4. Measurementsof remote angular sensi-tivity enhancement. (A)Normalized coincidencecount rates where one pho-ton is projected on diag-onal polarization, and thesecond photon is eitherkept polarization-encodedwhile the polarizer is ro-tated (green triangles) ortransferred to l = T10ℏ(blue diamonds), to l =T100ℏ (red squares), orto l = T300ℏ (black cir-cles) while the appropri-ate mask is rotated. Theerrors are estimated as-suming Poissonian countstatistics. (B) From thesteepest part of the fringes(0°), it is possible to cal-culate the correspondingangular sensitivity limitedby statistical fluctuationsfor different numbers ofdetected pairs. The dashedlines are the theoreticallyexpected sensitivities (as-suming 100% visibility and Poissonian fluctuation) and the points are the measured values. To illustratethe enhancement for 100 detected pairs, we measured the angular position of the randomly rotated maskby correcting the change in the coincidence counts with a rotation of the remote polarizer. The right panelshows histograms of 20 different random angles that were measured for each arrangement. For l =T300ℏ, the limit of our high-precision rotation stage (T0.016°) was determined with the polarizer in alow-precision mount (T1°). To reach the same precision without OAM-induced angular resolution en-hancement, about 3.3 million detected pairs would have been necessary.